Optimal Self-Dual Inequalities to Order Polarized BECs

Ting-Chun Lin, Hsin-Po Wang

$1-(1-x^M{)}^{2^M}>(1-(1-x{)}^M{)}^{2^M}$ is proved for all $x\in [0,1]$ and all $M>1$. This confirms a conjecture about polar code, made by Wu and Siegel in 2019, that $W^{0…